In a large skillet over medium heat, heat pan. Add oil and butter. Add chicken and season with salt and pepper. Cook until deeply golden, 7 to 8 minutes per side. Transfer to a plate.

Add chicken broth to skillet and deglaze pan, scraping up any brown bits with the bottom of a wooden spoon. Add shallot, garlic, and thyme to skillet and cook until fragrant, 2 minutes. Add potatoes and season with salt and pepper. Cover and cook 8 minutes.

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